Next generation cellular standards may leverage the large bandwidth available at millimeter wave (mm wave) frequencies to provide gigabit-per-second data rates in outdoor wireless systems. The main challenge in this high frequency band is to achieve high link margin. This challenge may be conquered using directional beamforming with large antenna arrays.
A conventional beam training protocol exhaustive search method is generally considered in tracking the angle of departure (AoD) and angle of arrival (AoA) for a MIMO channel. This method searches all possible beam directions for both the transmitter and the receiver. Referring to FIG. 1 as an example, for an antenna array of a transmitter end (Tx) and an antenna array of a receiver end (Rx) that have the same maximum resolution of N (where N=8 in FIG. 1), the complexity (steps) required for this method to adjust beamforming is N2 (=64, i.e., the 1st stage to the 64th stage in FIG. 1). However, this operation takes a long time and has high complexity.
Another conventional beam training method is called bisection method, which is proposed by A. Alkhateeb, O. El Ayach, G. Leus and R. Heath in “Channel estimation and hybrid precoding for millimeter wave cellular systems”, IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 831-846, 204, and which uses an adaptive algorithm to estimate the mm wave channel and alleviates the problem mentioned above. This bisection method is also referred to hereinafter as “the first conventional bisection method.” The bisection method performs angle estimation on the transmitter end and the receiver end at the same time. Referring to FIG. 2 as an example, for an antenna array of a transmitter end (Tx) and an antenna array of a receiver end (Rx) that have the same maximum resolution of N (where N=8 in FIG. 2), the method has a number log2 N (=log2 8=3 in FIG. 2) of bisection stages where four searching procedures are performed in each bisection stage. In detail, in the first bisection stage, the transmitter end (Tx) sequentially transmits two first-stage training signals respectively through two different first-stage Tx antenna sectors each having a size of π/2 by executing sector sweeping. At this time, the receiver end (Rx) also executes sector sweeping to sequentially receive the first-stage training signals respectively via two different first-stage Rx antenna sectors each having a size of π/2. The receiver end (Rx) selects one of the first-stage Rx antenna sectors via which the first-stage training signal received has better signal quality (e.g., higher signal-to-noise ratio, SNR) to serve as a first-stage candidate Rx antenna sector that corresponds to a specific receiver end antenna beam, and issues a first-stage feedback signal indicating one of the first-stage training signals that has better signal quality at the receiver end (Rx). Upon receipt of the first-stage feedback signal, the transmitter end (Tx) selects one of the first-stage Tx antenna sectors via which the first-stage training signal indicated by the first-stage feedback signal is transmitted to serve as a first-stage candidate Tx antenna sector that corresponds to a specific transmitter end antenna beam. Accordingly, in the first bisection stage, a number of steps of adjusting beamforming is four. In the second bisection stage, the transmitter end (Tx) sequentially transmits two second-stage training signals respectively through two different second-stage Tx antenna sectors each having a size of π/4 and each being bisected from the first-stage candidate Tx antenna sector, by executing sector sweeping. At this time, the receiver end (Rx) also executes sector sweeping to sequentially receive the second-stage training signals respectively via two different second-stage Rx antenna sectors each having a size of π/4 and each being bisected from the first-stage candidate Rx antenna sector. The receiver end (Rx) selects one of the second-stage Rx antenna sectors via which the second-stage training signal received has better signal quality to serve as a second-stage candidate Rx antenna sector, and issues a second-stage feedback signal indicating one of the second-stage training signals that has better signal quality at the receiver end (Rx). Upon receipt of the second-stage feedback signal, the transmitter end (Tx) selects one of the second-stage Tx antenna sectors via which the second-stage training signal indicated by the second-stage feedback signal is transmitted to serve as a second-stage candidate Tx antenna sector. Accordingly, in the second bisection stage, a number of steps of adjusting beamforming is four. In the third bisection stage, the transmitter end (Tx) sequentially transmits two third-stage training signals respectively through two different third-stage Tx antenna sectors each having a size of π/8 and each being bisected from the second-stage candidate Tx antenna sector, by executing sector sweeping. At this time, the receiver end (Rx) also executes sector sweeping to sequentially receive the third-stage training signals respectively via two different third-stage Rx antenna sectors each having a size of π/8 and each being bisected from the second-stage candidate Rx antenna sector. The receiver end (Rx) selects one of the third-stage Rx antenna sectors via which the third-stage training signal received has better signal quality to serve as a target Rx antenna sector (i.e., AOA), and issues a third-stage feedback signal indicating one of the third-stage training signals that has better signal quality at the receiver end (Rx). Upon receipt of the third-stage feedback signal, the transmitter end (Tx) selects one of the third-stage Tx antenna sectors via which the third-stage training signal indicated by the third-stage feedback signal is transmitted to serve as a target Tx antenna sector (i.e., AOD). Accordingly, in the third bisection stage, a number of steps of adjusting beamforming is four. As a result, the total number of steps of adjusting beamforming is 4 log2N (=4×3=12 in FIG. 2). In addition, the receiver end (Rx) has to issue the first-stage, second-stage and third-stage feedback signals respectively corresponding to the first, second and third bisection stages to the transmitter end (Tx), which means that three feedback operations are required.
U.S. Patent Application Publication Nos. 2016/0087695 and 2016/0021549 propose another bisection method that performs estimation separately on the transmitter end and the receiver end. This bisection method is also referred to hereinafter as “the second conventional bisection method.” In detail, the transmitter end first transmits the training signals while the receiver end operates in an omni-directional receiving mode to estimate the AoD, and then the AoA is estimated under a circumstance that the transmitter end operates at the AoD. Referring to FIG. 3 as an example, for an antenna array of a transmitter end (Tx) and an antenna array of a receiver end (Rx) that have the same maximum resolution of N (where N=8 in FIG. 3), the method has a number log2N (=log2 8=3 in FIG. 3) of bisection stages for each of the transmitter end (Tx) and the receiver end (Rx), where two searching procedures are performed for each of the transmitter end (Tx) and the receiver end (Rx) in each bisection stage. In detail, in the first Tx bisection stage, the transmitter end (Tx) sequentially transmits two first-stage training signals respectively through two different first-stage Tx antenna sectors each having a size of λ/2 and, by executing sector sweeping. At this time, the receiver end (Rx) omni-directionally and sequentially receives the first-stage training signals, and issues a first-stage feedback signal indicating one of the first-stage training signals that has better signal quality at the receiver end (Rx). Upon receipt of the first-stage feedback signal, the transmitter end (Tx) selects one of the first-stage Tx antenna sectors via which the first-stage training signal indicated by the first-stage feedback signal is transmitted to serve as a first-stage candidate Tx antenna sector. Accordingly, in the first Tx bisection stage, a number of steps of adjusting beamforming is two. In the second Tx bisection stage, the transmitter end (Tx) sequentially transmits two second-stage training signals respectively through two different second-stage Tx antenna sectors each having a size of π/4 and each being bisected from the first-stage candidate Tx antenna sector, by executing sector sweeping. At this time, the receiver end (Rx) omni-directionally and sequentially receives the second-stage training signals, and issues a second-stage feedback signal indicating one of the second-stage training signals that has better signal quality at the receiver end (Rx). Upon receipt of the second-stage feedback signal, the transmitter end (Tx) selects one of the second-stage Tx antenna sectors via which the second-stage training signal indicated by the second-stage feedback signal is transmitted to serve as a second-stage candidate Tx antenna sector. Accordingly, in the second Tx bisection stage, a number of steps of adjusting beamforming is two. In the third Tx bisection stage, the transmitter end (Tx) sequentially transmits two third-stage training signals respectively through two different third-stage Tx antenna sectors each having a size of π/8 and each being bisected from the second-stage candidate Tx antenna sector, by executing sector sweeping. At this time, the receiver end (Rx) omni-directionally and sequentially receives the third-stage training signals, and issues a third-stage feedback signal indicating one of the third-stage training signals that has better signal quality at the receiver end (Rx). Upon receipt of the third-stage feedback signal, the transmitter end (Tx) selects one of the third-stage Tx antenna sectors via which the third-stage training signal indicated by the third-stage feedback signal is transmitted to serve as a target Tx antenna sector (i.e., AoD). Accordingly, in the third Tx bisection stage, a number of steps of adjusting beamforming is two. In the first Rx bisection stage, the transmitter end (Tx) continuously transmits a training signal through the target Tx antenna sectors. At this time, the receiver end (Rx) executes sector sweeping to sequentially receive the training signal respectively via two different first-stage Rx antenna sectors each having a size of π/2. The receiver end (Rx) selects one of the first-stage Rx antenna sectors via which the training signal received has better signal quality to serve as a first-stage candidate Rx antenna sector. Accordingly, in the first Rx bisection stage, a number of steps of adjusting beamforming is two. In the second Rx bisection stage, the transmitter end (Tx) continuously transmits the training signal through the target Tx antenna sectors. At this time, the receiver end (Rx) executes sector sweeping to sequentially receive the training signal respectively via two different second-stage Rx antenna sectors each having a size of π/4 and each being bisected from the first-stage candidate Rx antenna sector. The receiver end (Rx) selects one of the second-stage Rx antenna sectors via which the training signal received has better signal quality to serve as a second-stage candidate Rx antenna sector. Accordingly, in the second Rx bisection stage, a number of steps of adjusting beamforming is two. In the third Rx bisection stage, the transmitter end (Tx) continuously transmits the training signal through the target Tx antenna sectors. At this time, the receiver end (Rx) executes sector sweeping to sequentially receive the training signal respectively via two different third-stage Rx antenna sectors each having a size of π/8 and each being bisected from the second-stage candidate Rx antenna sector. The receiver end (Rx) selects one of the third-stage Rx antenna sectors via which the training signal received has better signal quality to serve as a target Rx antenna sector (i.e., AoA). Accordingly, in the third Rx bisection stage, a number of steps of adjusting beamforming is two. As a result, the number of total steps of adjusting beamforming is 2 (log2 N+log2 N) (=2×(3+3)=12 in FIG. 3). In addition, the receiver end (Rx) has to issue the first-stage, second-stage and third-stage feedback signals respectively corresponding to the first, second and third Tx bisection stages to the transmitter end (Tx), which means that three feedback operations are required.